Concepedia

Descriptive set theory over hyperfinite sets

H. Jerome Keisler, Kenneth Kunen, Arnold W. Miller, Steven Leth

Journal of Symbolic Logic · 1989 · 36 citations · 7 references

DOI

Concepts

Abstract

Abstract The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.

References

7

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William A. Howard · Journal of Symbolic Logic · 1984 · 840 citations

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S. Ú. Maslov. Téoriá déduktivnyh sistém i éé priménéniá. Russian original of the preceding. Kibérnétika. Radio i Savz', Moscow 1986, 135 pp. - K. D. Stroyan and José Manuel Bayod. Foundations of infinitesimal stochastic analysis. Studies in logic and the foundations of mathematics, vol. 119. North-Holland, Amsterdam, New York, and Oxford, 1986, xii + 478 pp.

Nigel J. Cutland · Journal of Symbolic Logic · 1988 · 91 citations

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Analytic Sets, Baire Sets and the Standard Part Map

C. Ward Henson · Canadian Journal of Mathematics · 1979 · 55 citations · Full text

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The isomorphism property in nonstandard analysis and its use in the theory of Banach spaces

C. Ward Henson · Journal of Symbolic Logic · 1974 · 47 citations

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Unbounded Loeb measures

C. Ward Henson · Proceedings of the American Mathematical Society · 1979 · 27 citations · Full text

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